KKR & Co., the private-equity firm run by Henry Kravis and George Roberts, is cutting costs at its European portfolio companies to prepare for an economic slowdown as the debt crisis worsens, said the firm’s head of global capital.

“We’ve been bracing ourselves for companies to see a big pullback, so we’ve been taking out costs,” Scott Nuttall said today at the Keefe Bruyette & Woods Asset Management Conference in New York. “We’ve been trying to get as lean as we can.”

The crisis in Europe has hurt the value of companies owned by private-equity firms, and deal activity on the continent has been “relatively slow” as valuations fall and uncertainty rises, Nuttall said in April. Providence Equity Partners Inc., the buyout firm whose holdings include Univision Communications Inc. and the cable-television network of the New York Yankees, said investing in Europe is not worth the risk right now.

“Values don’t line up with risk and expected growth rates,” Jonathan Nelson, Providence’s chief executive officer and co-founder, said today at the SuperReturn conference in Boston.

Nuttall said KKR’s European companies are weathering the European turmoil better than expected because many of them have exports beyond the continent, including to Asian consumer markets.